Box and whiskers plot
Before studying this lesson, you need to understand
the median. Basically a box and whiskers plot looks like this:
Just like the name suggests, the rectangle you see is called a box.
Now the reason we call the two lines extending
from the edge of the box whiskers is simply because they look like whiskers or mustache, especially mustache of a cat
The five points or dot that you see represents the followings starting from left to right
Lower extreme: the lowest or smallest value in a set of data
Lower quartile or first quartile: the median of all data below the median
Median or second quartile: the middle value of the set of data. If there are two values in the middle, the median
is the average of the two values
Upper quartile or third quartile: the median of all data above the median
Upper extreme: The biggest value in the set
Example:
Construct a box and whiskers plot for the data set: {5, 2, 16, 9, 13, 7, 10}
First, you have to put the data set in order from greatest to least or from least to greatest
From least to greatest we get : 2 5 7 9 10 13 16
Since the smallest value in the set is 2, the lower extreme is
2
Since the greatest value in the set is 16, the upper extreme is
16
Now, look carefully at the set: 2 5 7
9 10 13 16
You can see that 9 is located right in the middle of the set of data
Therefore, 9 is the median
Now to get the lower quartile, you need all data before the median or 9
2 5 7 9 10 13 16
In bold right above we show all data before 9, so
2 5 7
Since the value in the middle for the set
2 5 7 is 5, the lower quartile is 5
Finally, to get the upper quartile, you need all data after the median or 9
2 5 7 9
10 13 16
In bold right above we show all data after 9, so
10 13 16
Since the value in the middle for the set
10 13 16 is 13, the upper quartile is 13
Now make a number line and graph above the number line 2, 5, 9, 13, and 16 with five dots: one dot will represent the median, one dot will represent each extreme,
finally, one dot will represent each quartile.
Your graph should look like this after you are done
Draw a rectangle or box starting from the lower quartile to the upper quartile. Draw a vertical segment too to represent
the median
Finally, draw horizontal segments or whiskers that connect all five dots together.
The box and whiskers plot for {5, 2, 16, 9, 13, 7, 10} is :

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